Multi-purpose sports arenas and stadia built around the world are often covered with space frames and lattice structures for weather protection, climate control, and acoustic enhancement. The basic shape of this type of cover, apart from local features of the surface, is usually a portion of a surface of a revolution, such as a portion of a sphere, cylinder, ellipsoid, and the like. Other kinds of surface contours have been and can be used.
One approach to the design of domes or arena roof covers is to use a single network comprised of interconnected structural members, or struts. The struts are located in and define the cover's basic contour surface. Further the struts subdivide the network into a lattice of triangular, rectangular, pentagonal, hexagonal or other polygonal areas. Note that the terms “network” and “surface” may be used interchangeably. Construction of the structural network is simplest when all of the struts in the network are of uniform depth.
However, single layer systems have limited span capabilities due to buckling. The buckling strength of a reticulated space frame is a function of the bending and axial stiffness of the system. For example, a single layer, double curvature aluminum system can span only up to about 400 feet and single layer, single curvature systems (vaults) are limited to about 200 feet. Moreover, these span capabilities are only for structures with relatively high rise-to-span ratio (e.g., 0.3 or higher). For flatter systems, the span capabilities are substantially reduced. In fact, for a single layer system, the buckling strength is inversely proportional to the surface radius of curvature (squared).
While in the past, roofs with high rise-to-span-ratio were acceptable to architects and designers, the current trend is to design arena roofs with low profiles. Low profile roofs have the advantage of minimizing the “amount of air under the roof” and therefore are more efficient from an HVAC design point of view. Additionally, many architects prefer low profile roof systems because of aesthetic considerations. High profile roof systems are undesirable from an aesthetic point of view because they become the predominant element of the building and become an obstacle to changing the building appearance. A low-rise roof system, on the other hand, allows architects to emphasize other elements of the structure.
Double network structures address many of the drawbacks and strength limitations associated with single network structures. In general, because of their higher bending stiffness, double network structures have higher buckling strength and much larger span capabilities than single network structures. As such, large span domes with low rise and large suspended equipment loads (as required by the modern sports arenas) may be safely designed and built using double layer systems. A single curvature double layer system can easily span up to 600 feet. The same system, but used in a structure with double curvature can span up to 900 feet.
U.S. Pat. No. 6,192,634 to Lopez, which is hereby incorporated by reference, describes an example of a double network structural system. The double network system has an inner structural network and an outer structural network. Each network has structural members or struts that are connected at junctions to define the lattice geometry and the shape of the structure. The system junctions have two plates, with the structural struts of each network fastened between top and bottom plates to form moment bearing junctions. Tubular braces are connected according to a desired arrangement between selected outer network junctions and selected inner network junctions. The tubular braces establish a substantially parallel spacing between the networks, and transfer primarily local loads between the networks. The network struts subdivide the outer and inner surfaces into polygonal areas, which are typically of a uniform kind in the outer network. The outer network openings can be closed by using closure panels which laterally stabilize the outer network struts and structurally enhance the network.
A similar double network dome is described in U.S. Pat. No. 5,704,169 to Richter, which is also hereby incorporated by reference. The basic shape of a large span dome in this patent is defined by an external network of structural struts which are so arranged between their junctions that they fully triangulate the surface of the dome. The struts throughout the network have substantially uniform cross-sectional dimensions and are sized to withstand the loads encountered at and near the perimeter of the dome. The central portion of the network is strengthened to withstand snap-through failure by means of a truss system comprised of an internal network and a system of trusses that connect the internal network to the dome outer surface. The internal network lies in a surface which is inside the dome and is uniformly spaced apart from the dome's triangulated surface. The external and internal networks are connected by tie struts which extend between connections at mid-span of inner surface struts and adjacent outer surface strut junctions and which lie in the planes defined by the webs of respective struts. The assembly of the tie struts to the strut junctions can be achieved by use of the same fasteners which connect the struts to their junctions.
The span capability of double layer structures, while greater than single layer structures, is still limited by a number of factors. These factors include the size of the upper layer struts, the size of the lower layer struts, the size of the diagonal struts, the frequency of the upper and lower layers, and the ability of the connections to transfer force. The ability of structural members and connections to transfer force is often the main factor limiting the span capability of systems such as those developed by Lopez and Richter.
In Richter and Lopez type systems, the pipes that connect the upper and lower layers rely on welded connections between the pipes and the triangular connector plates and they share the connection bolts of the main layer struts. Welding of aluminum is not only costly, but significantly weakens the parent metal and makes the area adjacent to the weld brittle. The allowable stresses of the heat-affected zone of a welded connection are typically reduced by 50% for aluminum. Furthermore, the pipe attachment method used by Lopez and Richter type systems results in a very crowded joint. The crowded joint limits the size of the pipe that can be used between the upper and lower networks. As such, these systems have limited capacity to transfer loads between networks (due to the reduced pipe size and welded connection strength), and have limited bending strength due to the system depth limitations that result directly from the pipe size limitation.
The limited load carrying capacity of the diagonal pipe strut connections in Richter and Lopez type systems limits the system depth and the ability of designers to optimize them. For example, the strut frequency of the upper layer (i.e., the number of struts in a given area) is controlled by the size and type of closure panels used. The lower layer, on the other hand, is not controlled by the closure panels and can often be of a lower strut frequency without sacrificing structural integrity. By reducing the lower layer frequency, the load carried per lower layer strut and by the diagonal connectors is increased, thereby making more efficient use of the struts and connectors. A system with a low load carrying capacity in one of its elements cannot be effectively optimized. An optimum double layer system is one that maximizes the load carrying capacity of the upper and lower layer struts, minimizes the number of diagonal connectors, minimizes the total number of joints and components, and makes efficient use of the load carrying capacity of the joints. As a result of the low load carrying capacity of the pipe connections, the use of Lopez and Richter type systems in the design of large span structures often result in structures that have a less than optimum number of joints and struts.
While existing double network designs address some of the problems associated with single network structures, the double network structures themselves are not without drawbacks and shortcomings. For example, presently available double network structures often make inefficient use of struts, joints, and network depth. These structures often contain more struts and joints than is required for the structure to maintain a sufficient degree of stability. In addition to making the structure heavier, the extraneous struts may increase the number of connections required at the nodal joints, resulting in an overly complicated system.
Accordingly, it is desirable to provide improved double layer systems that can expand the span capabilities and shape flexibility beyond those of existing single layer systems and to expand the span capabilities and efficiency beyond those of existing double layer systems. Specifically, it is desirable to provide a structural framing system that allows for optimization of the frequency of the lower layer network and connector grid and allows for minimization of the overall number of struts and joints, while maintaining the required degree of structural stability. In addition, the struts in such a structural framing system should be connected to each other in a manner so as to simplify the joints and assembly thereof.